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Coherent control of Rydberg states in silicon

Nature volume 465, pages 1057–1061 (2010)Cite this article

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Abstract

Laser cooling and electromagnetic traps have led to a revolution in atomic physics, yielding dramatic discoveries ranging from Bose–Einstein condensation to the quantum control of single atoms1. Of particular interest, because they can be used in the quantum control of one atom by another, are excited Rydberg states2,3,4, where wavefunctions are expanded from their ground-state extents of less than 0.1 nm to several nanometres and even beyond; this allows atoms far enough apart to be non-interacting in their ground states to strongly interact in their excited states. For eventual application of such states5, a solid-state implementation is very desirable. Here we demonstrate the coherent control of impurity wavefunctions in the most ubiquitous donor in a semiconductor, namely phosphorus-doped silicon. In our experiments, we use a free-electron laser to stimulate and observe photon echoes6,7, the orbital analogue of the Hahn spin echo8, and Rabi oscillations familiar from magnetic resonance spectroscopy. As well as extending atomic physicists’ explorations1,2,3,9 of quantum phenomena to the solid state, our work adds coherent terahertz radiation, as a particularly precise regulator of orbitals in solids, to the list of controls, such as pressure and chemical composition, already familiar to materials scientists10.

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Figure 1: The principle of the experiment.
Figure 2: Experimental orbital echo detection.
Figure 3: Rabi oscillations.
Figure 4: Comparison of hydrogen and Si:P, showing spectra and the principal excitation and decoherence mechanisms.

References

  1. Haeffner, H., Roos, C. F. & Blatt, R. Quantum computing with trapped ions. Phys. Rep. 469, 155–203 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  2. Urban, E. et al. Observation of Rydberg blockade between two atoms. Nature Phys. 5, 110–113 (2009)

    Article  ADS  CAS  Google Scholar 

  3. Gaëtan, A. et al. Observation of collective excitation of two individual atoms in the Rydberg blockade regime. Nature Phys. 5, 115–118 (2009)

    Article  ADS  Google Scholar 

  4. Schwarzschild, B. Experiments show blockading interaction of Rydberg atoms over long distances. Phys. Today 62, 15–18 (2009)

    Google Scholar 

  5. Stoneham, A. M., Fisher, A. J. & Greenland, P. T. Optically driven silicon-based quantum gates with potential for high-temperature operation. J. Phys. Condens. Matter 15, L447–L451 (2003)

    Article  ADS  CAS  Google Scholar 

  6. Abella, I. D., Kurnit, N. A. & Hartmann, S. R. Photon echoes. Phys. Rev. 141, 391–405 (1966)

    Article  ADS  CAS  Google Scholar 

  7. Allen, L. & Eberly, J. H. Optical Resonance and Two-level Atoms 195–220 (Dover, 1987)

    Google Scholar 

  8. Hahn, E. L. Spin echoes. Phys. Rev. 80, 580–594 (1950)

    Article  ADS  Google Scholar 

  9. Raitzsch, U. et al. Echo experiments in a strongly interacting Rydberg gas. Phys. Rev. Lett. 100, 013002 (2008)

    Article  ADS  Google Scholar 

  10. Tokura, Y. & Nagaosa, N. Orbital physics in transition-metal oxides. Science 288, 462–468 (2000)

    Article  ADS  CAS  Google Scholar 

  11. Zrenner, A. et al. Coherent properties of a two-level system based on a quantum dot photodiode. Nature 418, 612–614 (2002)

    Article  ADS  CAS  Google Scholar 

  12. Kroner, M. et al. Rabi splitting and ac-Stark shift of a charged exciton. Appl. Phys. Lett. 92, 031108 (2008)

    Article  ADS  Google Scholar 

  13. Kohn, W. & Luttinger, J. M. Theory of donor states in silicon. Phys. Rev. 98, 915–922 (1955)

    Article  ADS  CAS  Google Scholar 

  14. Karaiskaj, D., Stotz, J. A. H., Meyer, T., Thewalt, M. L. W. & Cardona, M. Impurity absorption spectroscopy in 28Si: the importance of inhomogeneous isotope broadening. Phys. Rev. Lett. 90, 186402 (2003)

    Article  ADS  CAS  Google Scholar 

  15. Vinh, N. Q. et al. Silicon as a model ion trap: time domain measurements of donor Rydberg states. Proc. Natl Acad. Sci. USA 105, 10649–10653 (2008)

    Article  ADS  CAS  Google Scholar 

  16. Tsyplenkov, V. V., Demidov, E. V., Kovalevski, K. A. & Shastin, V. N. Relaxation of excited donor states in silicon with emission of intervalley phonons. Semiconductors 42, 1016–1022 (2007)

    Article  ADS  Google Scholar 

  17. Oepts, D., van der Meer, A. F. G. & & van Amersfoort, P. W. The free electron laser facility FELIX. Infrared Phys. Technol. 36, 297–308 (1995)

    Article  ADS  CAS  Google Scholar 

  18. Shoemaker, R. L. in Laser and Coherence Spectroscopy (ed. Steinfeld, J. I.) 197–372 (Plenum, 1978)

    Book  Google Scholar 

  19. Agarwal, G. S. Quantum statistical theory of optical resonance phenomena in fluctuating laser fields. Phys. Rev. A 18, 1490–1506 (1978)

    Article  ADS  CAS  Google Scholar 

  20. Larsen, D. M. Concentration broadening of absorption lines from shallow donors in multivalley bulk semiconductors. Phys Rev B 67, 165204 (2003)

    Article  ADS  Google Scholar 

  21. Jagannath, C., Grabowski, Z. W. & Ramdas, A. K. Linewidths of the electronic excitation spectra of donors in silicon. Phys. Rev. B 23, 2082–2098 (1981)

    Article  ADS  CAS  Google Scholar 

  22. Brown, R. A. & Rodriguez, S. Low-temperature recombination of electrons and donors in n-type germanium and silicon. Phys. Rev. 153, 890–900 (1967)

    Article  ADS  CAS  Google Scholar 

  23. Ruess, F. J. et al. Towards atomic-scale device fabrication in silicon using scanning probe microscopy. Nano Lett. 4, 1969–1973 (2004)

    Article  ADS  CAS  Google Scholar 

  24. Petta, J. R. et al. Coherent manipulation of electron spins in semiconductor quantum dots. Science 309, 2180–2184 (2005)

    Article  ADS  CAS  Google Scholar 

  25. Knippels, G. M. H. et al. Generation and complete electric-field characterization of intense ultrashort tunable far-infrared laser pulses. Phys. Rev. Lett. 83, 1578–1581 (1999)

    Article  ADS  CAS  Google Scholar 

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Acknowledgements

We are grateful for conversations with A. J. Fisher, A. M. Stoneham, C. Kay and G. Morley; to R. Hulet for pointing out ref. 8; and for experimental assistance from K. Litvinenko and G. Morley. We acknowledge financial support from the Netherlands Organisation for Scientific Research and the Engineering and Physical Sciences Research Council (COMPASSS, grant reference EP/H026622/1, and Advanced Research Fellowship EP/E061265/1).

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Author notes

  1. N. Q. Vinh

    Present address: Present address: ITST, Department of Physics, University of California, Santa Barbara, California 93106-4170, USA.,

Authors and Affiliations

  1. London Centre for Nanotechnology and Department of Physics and Astronomy, University College London, London WC1H 0AH, UK

    P. T. Greenland, S. A. Lynch & G. Aeppli

  2. FOM Institute for Plasma Physics “Rijnhuizen”, PO Box 1207, NL-3430 BE Nieuwegein, The Netherlands,

    A. F. G. van der Meer, B. Redlich & N. Q. Vinh

  3. Advanced Technology Institute, University of Surrey, Guildford GU2 7XH, UK

    B. N. Murdin

  4. Department of Physics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, UK,

    C. R. Pidgeon

Authors
  1. P. T. Greenland
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  2. S. A. Lynch
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  3. A. F. G. van der Meer
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  5. C. R. Pidgeon
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  6. B. Redlich
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  7. N. Q. Vinh
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  8. G. Aeppli
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Contributions

N.Q.V. and C.R.P. initiated this work; P.T.G., S.A.L., B.N.M., N.Q.V. and G.A. designed the research programme; N.Q.V., P.T.G., S.A.L., A.F.G.v.d.M. and B.R. performed the experiments; P.T.G. performed the theory and analysis; and P.T.G., B.N.M., S.A.L. and G.A. wrote the paper.

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Correspondence to P. T. Greenland.

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The authors declare no competing financial interests.

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Greenland, P., Lynch, S., van der Meer, A. et al. Coherent control of Rydberg states in silicon. Nature 465, 1057–1061 (2010). https://doi.org/10.1038/nature09112

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